I've used GeoGebra.LCKurtz said:
I don't get what you are trying to say. If you try to draw the same picture with an angle of ##70^\circ## you don't get the lengths ##AH = AO##.ali PMPAINT said:
Oh, yes, you are right. For reasons, I thought any angle would be correctLCKurtz said:
So, you can continue by showing first portion A is equal to the third portion A, Then try to use trigonometry since AH=AO=R and AD=2R, and then you will get the answer.kaloyan said:
I'm 8th grade - I do not know Trigonometry.ali PMPAINT said:
What about similarity? It can be solved by it.(I don't know how is your country's education system)kaloyan said:
The orthocenter of a triangle is the point where all three of the triangle's altitudes intersect. An altitude is a line that passes through a vertex of the triangle and is perpendicular to the opposite side.
The orthocenter of a triangle can be found by constructing the altitudes of the triangle and finding their point of intersection. Alternatively, it can also be found by using the formula: Orthocenter = (a^2h_a + b^2h_b + c^2h_c)/(a^2 + b^2 + c^2), where a, b, and c are the side lengths of the triangle and h_a, h_b, and h_c are the altitudes.
The centroid of a triangle is the point where all three of the triangle's medians intersect. A median is a line that passes through a vertex of the triangle and the midpoint of the opposite side. The orthocenter and centroid of a triangle are always collinear, meaning they lie on the same line. The centroid divides the line segment between the orthocenter and the vertex in a ratio of 2:1.
A triangle can have only one orthocenter. This is because the three altitudes of a triangle are always concurrent, meaning they intersect at one point. Therefore, the orthocenter is a unique point for every triangle.
The orthocenter is an important point in triangle geometry because it is related to other important points such as the centroid, circumcenter, and incenter. It is also used in various theorems and constructions, such as the construction of the Euler line and the proof of the orthocenter theorem. Additionally, the orthocenter helps to define the orthic triangle, which is formed by the feet of the altitudes of a triangle.